Set theory and logic / by Robert R. Stoll.
Series A series of undergraduate books in mathematicsEditor: San Francisco : W. H. Freeman, c1961, c1963Descripción: xiv, 474 p. ; 24 cmOtro título: Introduction to set theory and logic [Título de cubierta]Otra clasificación: 03-01Chapter 1 SETS AND RELATIONS [1] 1. Cantor’s Concept of a Set [2] 2. The Basis of Intuitive Set Theory [4] 3. Inclusion [9] 4. Operations for Sets [12] 5. The Algebra of Sets [16] 6. Relations [23] 7. Equivalence Relations [29] 8. Functions [34] 9. Composition and Inversion for Functions [38] 10. Operations for Collections of Sets [43] 11. Ordering Relations [48] Chapter 2 THE NATURAL NUMBER SEQUENCE AND ITS GENERALIZATIONS [56] 1. The Natural Number Sequence [57] 2. Proof and Definition by Induction [70] 3. Cardinal Numbers [79] 4. Countable Sets [87] 5. Cardinal Arithmetic [95] 6. Order Types [98] 7. Well-ordered Sets and Ordinal Numbers [102] 8. The Axiom of Choice, the Well-ordering Theorem, and Zorn’s Lemma [111] 9. Further Properties of Cardinal Numbers [118] 10. Some Theorems Equivalent to the Axiom of Choice [124] 11. The Paradoxes of Intuitive Set Theory [126] Chapter 3 THE EXTENSION OF THE NATURAL NUMBERS TO THE REAL NUMBERS [130] 1. The System of Natural Numbers [130] 2. Differences [132] 3. Integers [134] 4. Rational Numbers [137] 5. Cauchy Sequences of Rational Numbers [142] 6. Real Numbers [149] 7. Further Properties of the Real Number System [154] Chapter 4 LOGIC [160] 1. The Statement Calculus. Sentential Connectives [160] 2. The Statement Calculus. Truth Tables [164] 3. The Statement Calculus. Validity [169] 4. The Statement Calculus. Consequence [179] 5. The Statement Calculus. Applications [187] 6. The Predicate Calculus. Symbolizing Everyday Language [192] 7. The Predicate Calculus. A Formulation [200] 8. The Predicate Calculus. Validity [205] 9. The Predicate Calculus. Consequence [215] Chapter 5 INFORMAL AXIOMATIC MATHEMATICS [221] 1. The Concept of an Axiomatic Theory [221] 2. Informal Theories [227] 3. Definitions of Axiomatic Theories by Set-theoretical Predicates [233] 4. Further Features of Informal Theories [236] Chapter 6 BOOLEAN ALGEBRAS [248] 1. A Definition of a Boolean Algebra [248] 2. Some Basic Properties of a Boolean Algebra [250] 3. Another Formulation of the Theory [254] 4. Congruence Relations for a Boolean Algebra [259] 5. Representations of Boolean Algebras [267] 6. Statement Calculi as Boolean Algebras [273] 7. Free Boolean Algebras [274] 8. Applications of the Theory of Boolean Algebras to Statement Calculi [278] 9. Further Interconnections between Boolean Algebras and Statement Calculi [282] Chapter 7 INFORMAL AXIOMATIC SET THEORY [289] 1. The Axioms of Extension and Set Formation [289] 1. The Axiom of Pairing [292] 3. The Axioms of Union and Power Set [294] 4. The Axiom of Infinity [297] 5. The Axiom of Choice [302] 6. The Axiom Schemas of Replacement and Restriction [302] 7. Ordinal Numbers [306] 8. Ordinal Arithmetic [312] 9. Cardinal Numbers and Their Arithmetic [316] 10. The von Neumann-Bernays-Gödel Theory of Sets [318] Chapter 8 SEVERAL ALGEBRAIC THEORIES [321] 1. Features of Algebraic Theories [322] 2. Definition of a Semigroup [324] 3. Definition of a Group [329] 4. Subgroups [333] 5. Coset Decompositions and Congruence Relations for Groups [339] 6. Rings, Integral Domains, and Fields [346] 7. Subrings and Difference Rings [351] 8. A Characterization of the System of Integers [357] 9. A Characterization of the System of Rational Numbers [361] 10. A Characterization of the Real Number System [367] FIRST-ORDER THEORIES [373] 1. Formal Axiomatic Theories [373] 2. The Statement Calculus as a Formal Axiomatic Theory [375] 3. Predicate Calculi of First Order as Formal Axiomatic Theories [387] 4. First-order Axiomatic Theories [394] 5. Metamathematics [401] 6. Consistency and Satisfiability of Sets of Formulas [409] 7. Consistency, Completeness, and Categoricity of First-order Theories [417] 8. Turing Machines and Recursive Functions [426] 9. Some Undecidable and Some Decidable Theories [436] 10. Gödel’s Theorems [446] 11. Some Further Remarks about Set Theory [452] References [457] Symbols and Notation [465] Author Index [467] Subject Index [469]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 03 St875 (Browse shelf) | Available | A-1417 |
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| 03 St817 Unvollständigkeit und Unentscheidbarkeit : | 03 St839 Matrix logic and mind : | 03 St873 Some combinatorial and algorithmic problems in many-valued logics / | 03 St875 Set theory and logic / | 03 St927 Structure, method and meaning : | 03 St933 Studies in model theory / | 03 St933a Studies in algebraic logic / |
Chapter 1 SETS AND RELATIONS [1] --
1. Cantor’s Concept of a Set [2] --
2. The Basis of Intuitive Set Theory [4] --
3. Inclusion [9] --
4. Operations for Sets [12] --
5. The Algebra of Sets [16] --
6. Relations [23] --
7. Equivalence Relations [29] --
8. Functions [34] --
9. Composition and Inversion for Functions [38] --
10. Operations for Collections of Sets [43] --
11. Ordering Relations [48] --
Chapter 2 THE NATURAL NUMBER SEQUENCE --
AND ITS GENERALIZATIONS [56] --
1. The Natural Number Sequence [57] --
2. Proof and Definition by Induction [70] --
3. Cardinal Numbers [79] --
4. Countable Sets [87] --
5. Cardinal Arithmetic [95] --
6. Order Types [98] --
7. Well-ordered Sets and Ordinal Numbers [102] --
8. The Axiom of Choice, the Well-ordering Theorem, and Zorn’s Lemma [111] --
9. Further Properties of Cardinal Numbers [118] --
10. Some Theorems Equivalent to the Axiom of Choice [124] --
11. The Paradoxes of Intuitive Set Theory [126] --
Chapter 3 THE EXTENSION OF THE NATURAL NUMBERS TO THE REAL NUMBERS [130] --
1. The System of Natural Numbers [130] --
2. Differences [132] --
3. Integers [134] --
4. Rational Numbers [137] --
5. Cauchy Sequences of Rational Numbers [142] --
6. Real Numbers [149] --
7. Further Properties of the Real Number System [154] --
Chapter 4 LOGIC [160] --
1. The Statement Calculus. Sentential Connectives [160] --
2. The Statement Calculus. Truth Tables [164] --
3. The Statement Calculus. Validity [169] --
4. The Statement Calculus. Consequence [179] --
5. The Statement Calculus. Applications [187] --
6. The Predicate Calculus. Symbolizing --
Everyday Language [192] --
7. The Predicate Calculus. A Formulation [200] --
8. The Predicate Calculus. Validity [205] --
9. The Predicate Calculus. Consequence [215] --
Chapter 5 INFORMAL AXIOMATIC MATHEMATICS [221] --
1. The Concept of an Axiomatic Theory [221] --
2. Informal Theories [227] --
3. Definitions of Axiomatic Theories by --
Set-theoretical Predicates [233] --
4. Further Features of Informal Theories [236] --
Chapter 6 BOOLEAN ALGEBRAS [248] --
1. A Definition of a Boolean Algebra [248] --
2. Some Basic Properties of a Boolean Algebra [250] --
3. Another Formulation of the Theory [254] --
4. Congruence Relations for a Boolean Algebra [259] --
5. Representations of Boolean Algebras [267] --
6. Statement Calculi as Boolean Algebras [273] --
7. Free Boolean Algebras [274] --
8. Applications of the Theory of Boolean Algebras to Statement Calculi [278] --
9. Further Interconnections between Boolean Algebras and Statement Calculi [282] --
Chapter 7 INFORMAL AXIOMATIC SET THEORY [289] --
1. The Axioms of Extension and Set Formation [289] --
1. The Axiom of Pairing [292] --
3. The Axioms of Union and Power Set [294] --
4. The Axiom of Infinity [297] --
5. The Axiom of Choice [302] --
6. The Axiom Schemas of Replacement and Restriction [302] --
7. Ordinal Numbers [306] --
8. Ordinal Arithmetic [312] --
9. Cardinal Numbers and Their Arithmetic [316] --
10. The von Neumann-Bernays-Gödel Theory of Sets [318] --
Chapter 8 SEVERAL ALGEBRAIC THEORIES [321] --
1. Features of Algebraic Theories [322] --
2. Definition of a Semigroup [324] --
3. Definition of a Group [329] --
4. Subgroups [333] --
5. Coset Decompositions and Congruence Relations for Groups [339] --
6. Rings, Integral Domains, and Fields [346] --
7. Subrings and Difference Rings [351] --
8. A Characterization of the System of Integers [357] --
9. A Characterization of the System of Rational Numbers [361] --
10. A Characterization of the Real Number System [367] --
FIRST-ORDER THEORIES [373] --
1. Formal Axiomatic Theories [373] --
2. The Statement Calculus as a Formal Axiomatic Theory [375] --
3. Predicate Calculi of First Order as Formal Axiomatic Theories [387] --
4. First-order Axiomatic Theories [394] --
5. Metamathematics [401] --
6. Consistency and Satisfiability of Sets of Formulas [409] --
7. Consistency, Completeness, and Categoricity of First-order Theories [417] --
8. Turing Machines and Recursive Functions [426] --
9. Some Undecidable and Some Decidable Theories [436] --
10. Gödel’s Theorems [446] --
11. Some Further Remarks about Set Theory [452] --
References [457] --
Symbols and Notation [465] --
Author Index [467] --
Subject Index [469] --
MR, 30 #11
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